# Pinned or moving: states of a single shock in a ring

## TL;DR

This paper investigates how shocks in a ring-shaped exclusion process can be either pinned or moving, revealing smooth transitions between these states through combined theoretical and simulation approaches, with implications for biological transport.

## Contribution

It introduces a model combining driven and diffusive segments to control shock localization, bridging behaviors seen in open and ring systems.

## Key findings

- Smooth transition between pinned and moving shocks observed
- Diffusive segment fluctuations control shock behavior
- Mean-field and Monte Carlo methods characterize steady states

## Abstract

Totally asymmetric exclusion processes (TASEP) with open boundaries are known to exhibit moving shocks or delocalised domain walls (DDW) for sufficiently small equal injection and extraction rates. In contrast TASEPs in an inhomogeneous ring have been shown to display pinned shocks or localised domain walls (LDW) under similar conditions [see, e.g., H. Hinsch and E. Frey, {\em Phys. Rev. Lett.} {\bf 97}, 095701 (2006)]. By studying periodic exclusion processes composed of a driven (TASEP) and a diffusive segments, we uncover smooth transitions between LDW and DDW; the latter mimics DDWs in an open TASEP, controlled essentially by the fluctuations in the diffusive segment. Mean-field theory together with Monte Carlo simulations are employed to characterize the emerging nonequilibrium steady states. Our studies provide an explicit route to control the degree of shock fluctuations in periodic systems, and should be relevant in cell biological transport where the availability of molecular motors is the rate limiting constraint.